Fractal behaviours of networks induced on infinite tree structures by random walks

Tree graphs such as Cayley trees provide a stage to support the self-organization of fractal networks by the flow of walkers from the root vertex to the outermost shell of the tree graph. This network model is a typical example that demonstrates the ability of a random process on a network to generate fractality. However, the finite scale of the tree structure assumed in the model restricts the size of fractal networks. In this study, we removed the restriction on the size of the trees by introducing a lifetime τ (number of steps of random walks) of walkers. As a result, we successfully induced a size-independent fractal structure on a tree graph without a boundary. Our numerical results show that the mean number of offspring d b of the original tree structure determines the value of the fractal box dimension db through the relation d b — 1 = (n b — 1) -θ . The lifetime τ controls the presence or absence of small-world and scale-free properties. The ideal fractal behaviour can be maintained by selecting an appropriate value of τ. The numerical results contribute to the development of a systematic method for generating fractal small-world and scale-free networks while controlling the value of the fractal box dimension. Unlike other models that use recursive rules to generate self-similar structures, this model specifically produces small-world fractal networks with scale-free properties.

Taxallnomy: an extension of NCBI Taxonomy that produces a hierarchically complete taxonomic tree

Background NCBI Taxonomy is the main taxonomic source for several bioinformatics tools and databases since all organisms with sequence accessions deposited on INSDC are organized in its hierarchical structure. Despite the extensive use and application of this data source, an alternative representation of data as a table would facilitate the use of information for processing bioinformatics data. To do so, since some taxonomic-ranks are missing in some lineages, an algorithm might propose provisional names for all taxonomic-ranks. Results To address this issue, we developed an algorithm that takes the tree structure from NCBI Taxonomy and generates a hierarchically complete taxonomic table, maintaining its compatibility with the original tree. The procedures performed by the algorithm consist of attempting to assign a taxonomic-rank to an existing clade or “no rank” node when possible, using its name as part of the created taxonomic-rank name (e.g. Ord_Ornithischia) or interpolating parent nodes when needed (e.g. Cla_of_Ornithischia), both examples given for the dinosaur Brachylophosaurus lineage. The new hierarchical structure was named Taxallnomy because it contains names for all taxonomic-ranks, and it contains 41 hierarchical levels corresponding to the 41 taxonomic-ranks currently found in the NCBI Taxonomy database. From Taxallnomy, users can obtain the complete taxonomic lineage with 41 nodes of all taxa available in the NCBI Taxonomy database, without any hazard to the original tree information. In this work, we demonstrate its applicability by embedding taxonomic information of a specified rank into a phylogenetic tree and by producing metagenomics profiles. Conclusion Taxallnomy applies to any bioinformatics analyses that depend on the information from NCBI Taxonomy. Taxallnomy is updated periodically but with a distributed PERL script users can generate it locally using NCBI Taxonomy as input. All Taxallnomy resources are available at http://bioinfo.icb.ufmg.br/taxallnomy.

Manipulating Chain Type and Flail Drum Speed for Better Fibre Recovery in Chain-Flail Delimber-Debarker-Chipper Operations

A chain-flail delimber-debarker-chipper (CFDDC) was adapted for treating smaller trees than normal by replacing the standard flails with lighter ones, and by reducing flail drum rotation speed. The machine produced 16 full containers (24 t each) for the standard configuration and 24 full containers for the innovative one. For each container the researchers measured: original tree mass, chip mass, time consumption and fuel use. Results indicated that the innovative setting accrued a 12% improvement on fiber recovery compared with the standard setting (control). At the same time, productivity increased by 20% and fuel consumption was reduced by 30%. Product quality was largely unaffected, with bark content remaining below the 1% threshold specification. If at all, product quality was improved through the reduction of fine particles, possibly derived from less diffused fraying. These results have triggered the real scale adoption of the new setting by contractors who participated in the study. The success of the innovative treatment is likely explained by its better alignment with the weaker structure of small trees from low-yielding stands.

THE BAOBAB TREE

Trees are known to live for many years. Gautama Buddha attained enlightenment while meditating underneath a peepal tree (Ficus religiosa). A branch of the original tree was rooted in Anuradhapura, Sri Lanka in 288 B.C. and is known as Jaya Sri Maha Bodhi. It is the oldest plant in the world. Long-living plants are found in many parts of the world. The Baobab tree is one among them. Baobab is the common name of a genus of trees (Adansonia) distributed in Madagascar, Africa, Australia and India. The Baobab is the national tree of Madagascar. The Baobab is also known as “bottle tree”, “the tree of life”, “upside-down tree”, and “monkey bread tree”.

Growth of Norway spruce (Picea abies [L.] Karsten) from artificial and natural regeneration in the Krkonoše Mts. and air temperature variability

Our research was concerned with a description of the influence of variability in average temperatures on the height growth of selected young populations of spruce in the Krkonoše Mts. Several populations of spruce were evaluated while the majority of them originated by natural regeneration on plots under disturbance of the original tree layer. In addition, several planted spruce populations in similar environmental conditions were also evaluated. The main questions of this study are as follows: is there a difference in height growth between populations of natural and artificial origin? Is it possible to find a relationship between height growth and climate feature during the last several years? The growth of young spruce populations that originated by natural regeneration was different from the growth of the planted populations. The average air temperature in the growing period, estimated as average temperature during the months of May to August, was proved to have a significant influence on year-on-year variability in spruce growth. Based on this finding, it was possible to estimate an increase in the height increment of young spruce caused by warming up since the mid-70s of the 20^th century to equal approximately 16% per decade in the spruce altitudinal zone in the Krkonoše Mts.  

WOOD IDENTIFICATION IN THE CAPPELLA PALATINA CEILING (12th CENTURY) IN PALERMO (SICILY, ITALY)

Anatomical studies were made on the structural and decorative elements of the wooden ceiling of the 12th century Cappella Palatina in Palermo, Sicily, to identify the timbers used, analyse their likely provenance, and discuss the selection criteria used by the builders. One hundred and fifty fragments were examined. Abies sp., Pinus sp., Betula sp., Populus sp. and Fagus sylvatica were found and all are most probably from Sicily. Some of the Abies fragments probably belong to Abies nebrodensis as they have exceptionally long tracheids, very tall rays, and abundant crystals. This species was over-Iogged in the past and now only 29 trees remain in the Madonie Natural Reserve in Sicily. Abies and Pinus are found in vertieal and horizontal painted panels, while Populus, Betula and Fagus were used in smaller parts of the muqarnas (painted niches). The choice of species seems to have been related to original tree size. The large size of the Abies boles meant that quarter sawn panels could be used. Sieilian Abies was highly valued at that time for its wood quality.Special attention was paid to the problem of distinguishing partly degraded Abies and Cedrus woods. However, the scalloped torus in some sampies displayed ambiguous features and these sampies were therefore classified as Abies/Cedrus.

On the number of vertices with a given degree in a Galton-Watson tree

Let Yk(ω) (k ≥ 0) be the number of vertices of a Galton-Watson tree ω that have k children, so that Z(ω) := ∑k≥0Yk(ω) is the total progeny of ω. In this paper, we will prove various statistical properties of Z and Yk. We first show, under a mild condition, an asymptotic expansion of P(Z = n) as n → ∞, improving the theorem of Otter (1949). Next, we show that Yk(ω) := ∑j=0kYj(ω) is the total progeny of a new Galton-Watson tree that is hidden in the original tree ω. We then proceed to study the joint probability distribution of Z and Ykk, and show that, as n → ∞, Yk/nk is asymptotically Gaussian under the conditional distribution P(· | Z = n).

On the number of vertices with a given degree in a Galton-Watson tree

Let Y k (ω) (k ≥ 0) be the number of vertices of a Galton-Watson tree ω that have k children, so that Z(ω) := ∑ k≥0 Y k (ω) is the total progeny of ω. In this paper, we will prove various statistical properties of Z and Y k . We first show, under a mild condition, an asymptotic expansion of P(Z = n) as n → ∞, improving the theorem of Otter (1949). Next, we show that Y k (ω) := ∑ j=0 k Y j (ω) is the total progeny of a new Galton-Watson tree that is hidden in the original tree ω. We then proceed to study the joint probability distribution of Z and Y k k , and show that, as n → ∞, Y k /n k is asymptotically Gaussian under the conditional distribution P(· | Z = n).